New Universality Classes for Two-Dimensional $\sigma$-Models

Abstract

We argue that the two-dimensional $O(N)$-invariant lattice $\sigma$-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum $\sigma$-model constructed by conventional perturbation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for $N=3,4$ on lattices up to $512\times 512$, using a Wolff-type embedding algorithm. [CPU time $\approx$ 7 years IBM RS-6000/320H] The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the $R{P}^{N-1}$ and $N$-vector models do not lie in the same universality class.

Comments: 10 pages (includes 2 figures), 211176 bytes Postscript, NYU-TH-93/07/03, IFUP-TH 34/93